2-This uncertainty which is present in any
real measurement arises from the fact that any imaginable measuring
device--even if designed and used perfectly---can record its measurement only
with a finite precision.

3-One way to understand this fact is to
realize that in order to record a measurement with infinite precision, the
instrument would require an output capable of displaying an infinite number of
digits.

4-By using more accurate measuring devices,
uncertainty in measurements can often be made as small as needed for a
particular purpose, but it can never be eliminated completely, even as a
theoretical idea.

6-In the study of motion using Newton's
laws, the uncertainty present in the initial conditions of a system yields a
corresponding uncertainty, however small, in the range of the prediction for
any later or earlier time.

7-Throughout most of the modern history of
physics, it has been assumed that it is possible to shrink the uncertainty in
the final dynamical prediction by measuring the initial conditions to greater
and greater accuracy.

9-It is important to remember that the
uncertainty in the dynamical outcome does not arise from any randomness in the
equations of motion--since they are completely deterministic--but rather from
the lack of the infinite accuracy in the initial conditions.

10-The unspoken goal of experimental science
has been that as measuring instruments become more and more accurate through
technology, the accuracy of the predictions made by applying the dynamical laws
will become greater and greater, approaching but never reaching absolute
accuracy.